Problem writeup

Goals:

  • To increase your understanding of the classical theory of fields by immersing yourself in a difficult question and having to explain your reasoning to a greater extent than on a homework problem.
  • To work on communicating your ideas.
  • To work on communicating your ideas in a scientific context.

Here's how it works for a writeup:

Chose a problem to write up in more detail. These should be:

  • Pick a problem from the ones at the end of chapters in Griffiths. These end of chapter problems tend to synthesize concepts more than the problems embeded in the chapter.
  • I'll give a bit of a bonus for harder-than-average problems.
  • Pick one from chapter 2 onwards.
  • Not problems that were assigned for another purpose.
  • Pick your own problem to work. I'll have a signup "sheet" on Moodle so you can see what problems other students are doing.

You *may* consult other people and resources about your problem. But you will write up your problem yourself. The same standards for homework problems--using citations and not consulting online solutions to your particular problem--apply.

Feedback and revision are important parts of the writing process. You will:

  1. Hand in a first draft of your problem writeup,
  2. (Tele-)Conference with Paul about your first draft. This conference will count towards the final exam: An oral part of the final exam. So, the focus on of your first draft should be on solving the problem, and being able to explain your solution orally. For the "exam portion", rubric elements (below) such as spelling, grammar, proper math typography will not count!
  3. You'll revise your first draft and hand in a final draft of the problem. And of course the final draft is where all the rubric elements (below) will be graded for your project grade.

You'll use CoCalc.com or Mathematica to write up a solution with equations, diagrams as appropriate, and text which explains the approach you took to the problem, and references the physical principles you're using.

The rubric used to grade this assignment comprises these categories:

  • Exposition of the problem - Copy out the statement of the problem. Use a different font to visually distinguish your work from the specification of the problem (e.g. italic, or different font-face). Label the problem with chapter and problem number.

  • Diagrams and plots - Use a diagram to sketch out the physical system, and label the names of quantities (angles, coordinates, etc). You may hand draw this! Include plots of functions as appropriate, for example to indicate maxima or minima, or equipotentials, or a potential energy surface, or otherwise enlighten the problem in some way.

  • Grammar and spelling - Use a more formal voice than when speaking, e.g. "a maxima" not "a max", "substitute in" rather than "plug in". Punctuation in physics papers is a unique issue. You should punctuate equations as if they were any other part of your writing: periods or commas frequently go at the end of a displayed equation.

  • Correctness of your solution - Gotta make sure you do the problem right! Include some sort of "sanity check" on your results. That is, estimate the answer by some other means than what you used to solve it exactly, or test your answer at limits where you're pretty sure of the answer to make sure it behaves as you think it should.

  • Clarity of narration - Think of your audience as other students in this class, with some general familiarity with the material. Name the principles and techniques you're using to solve the problem at each section of your problem. You may refer to equations in the textbook: give some context to say where such an equation comes from.

    It is a common error to take for granted the vector nature of key quantities. The electric field is *always* a vector field with 3 components that depend on the 3 components of position (and possibly time as well: $\myv E(\myv r)$. We frequently make symmetry arguments to argue that the electric field has some simpler form. For example, the field around a charge at the origin has spherical symmetry, which means that $\myv E(r,\theta,\phi) = E_r(r) \uv r$. Once you point this out, you can start throwing around "$E(r)$" but not before you point out how $E(r)$ is related to the full vector field.

  • Math typesetting / notation - Use real subscripts (not t0 when you mean $t_0$). Figure out how to get greek letters in Mathematica. (Esc-a-esc results in $\alpha$. Esc-q-esc $\to \theta$. Distinguish visually between vector and scalar quantities: scalars are usually displayed as non-bold italic quantities (Mathematica should do this automatically in math mode). Vector quantities are generally non-italic, and either have a little arrow over them, e.g. $\myv{b}$, or else appear as bold face, e.g. $\bf{b}$. Mathematica commands will generally appear as a monospaced font like this "Plot[ Sin[x],......]" without you having to do anything special. When displaying definite integrals, use the ' notation to distinguish between the integration variable and the integration limits, e.g. $$\int_{v_0}^{v(t)} \frac{dv'}{F(v')}.$$ You don't have to (though you may) number every equation. But you should have *some* system (even if it's only a hand lettered "star" beside an equation) for referring to particular equations from your text.